Trace formula for interacting spins

Abstract

While detailed information about the semiclassics for single-particle systems is available, much less is known about the connection between quantum and classical dynamics for many-body systems. As an example, we focus on interacting spins, which are of considerable conceptual and practical importance. We derive a trace formula for coupled spin j particles which relates the quantum energy levels to the classical dynamics. Our derivation is valid in the limit with and applies to time-continuous as well as to periodically driven dynamics. We provide a simple explanation why the Solari–Kochetov phase can be omitted if the correct classical Hamiltonian is chosen.